Haven't seen a discussion post for the new special, so I'll get the ball rolling. Thoughts, insights, bits you loved... let it all out.
Here's how I interpreted that scene:
The TARDIS knows how Donna was fired, it knows she's a bit clutzy, and it knows she takes subliminal suggestion, especially after being recently demetacrisised. It also misses her and needs her to stay with the Doctor for a while longer. So, predictably, Donna spills her coffee on the console, and the TARDIS is all like WHOOAAAA, oh my, I'm falling, I'm on fire, look at the sparks, we could go anywhere!! Heehee.